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I'd rent winter rubber for under 300 euro and enjoy your new ride. I've done several winter ED's, including a great romp in Scotland, and in some ways preferred the winter trips.
Taking the DE .50 with you is not advised

Rent the winter tires, unless your plans are extremely flexible and you don't mind being stuck at one place for a few days or altering your plans to avoid winter weather.

I went to do European Delivery in late April and it was still plenty cold. We ended up getting a few inches of snow in Berchtesgaden, and I was concerned for a few hours that we may be stranded at the Intercontinental .

An advantage also is that you'll have fresh rubber when your car is returned stateside, which offsets the cost somewhat.

I'd rent winter rubber for under 300 euro and enjoy your new ride. I've done several winter ED's, including a great romp in Scotland, and in some ways preferred the winter trips.
Taking the DE .50 with you is not advised